The physics of hearing: fluid mechanics and the active process of the inner ear

Abstract

Most sounds of interest consist of complex, time-dependent admixtures of tones of diverse frequencies and variable amplitudes. To detect and process these signals, the ear employs a highly nonlinear, adaptive, real-time spectral analyzer: the cochlea. Sound excites vibration of the eardrum and the three miniscule bones of the middle ear, the last of which acts as a piston to initiate oscillatory pressure changes within the liquid-filled chambers of the cochlea. The basilar membrane, an elastic band spiraling along the cochlea between two of these chambers, responds to these pressures by conducting a largely independent traveling wave for each frequency component of the input. Because the basilar membrane is graded in mass and stiffness along its length, however, each traveling wave grows in magnitude and decreases in wavelength until it peaks at a specific, frequency-dependent position: low frequencies propagate to the cochlear apex, whereas high frequencies culminate at the base. The oscillations of the basilar membrane deflect hair bundles, the mechanically sensitive organelles of the ear's sensory receptors, the hair cells. As mechanically sensitive ion channels open and close, each hair cell responds with an electrical signal that is chemically transmitted to an afferent nerve fiber and thence into the brain. In addition to transducing mechanical inputs, hair cells amplify them by two means. Channel gating endows a hair bundle with negative stiffness, an instability that interacts with the motor protein myosin-1c to produce a mechanical amplifier and oscillator. Acting through the piezoelectric membrane protein prestin, electrical responses also cause outer hair cells to elongate and shorten, thus pumping energy into the basilar membrane's movements. The two forms of motility constitute an active process that amplifies mechanical inputs, sharpens frequency discrimination, and confers a compressive nonlinearity on responsiveness. These features arise because the active process operates near a Hopf bifurcation, the generic properties of which explain several key features of hearing. Moreover, when the gain of the active process rises sufficiently in ultraquiet circumstances, the system traverses the bifurcation and even a normal ear actually emits sounds. The remarkable properties of hearing thus stem from the propagation of traveling waves on a nonlinear and excitable medium.

Reticular lamina and basilar membrane vibrations in living mouse cochleae

“…Active differential movements of the reticular lamina could therefore result in longitudinal fluid movements. As the traveling waves propagate forward, these longitudinal fluid movements help transfer energy toward best-frequency locations (6,36) (Fig. 4G), boosting the peak response.…”

“…The cochlea's remarkable sensitivity is commonly attributed to a micromechanical feedback system, which amplifies soft sounds using forces generated by outer hair cells (2)(3)(4)(5)(6)(7)(8)(9)(10). In addition to active bundle movements (2), mammalian outer hair cells are capable of changing their lengths in response to electrical stimulation in vitro (11)(12)(13)(14).…”

Timing of the reticular lamina and basilar membrane vibration in living gerbil cochleae

“…In response to the membrane potential change, mammalian outer hair cells change their length and generate force primarily through the somatic motility driven by the motor protein, prestin (Ashmore, 2008; Brownell et al, 1985; Liberman et al, 2002; Mammano and Ashmore, 1993; Mellado Lagarde et al, 2008; Ren et al, 2016a; Santos-Sacchi, 1989; Zheng et al, 2000). This cellular force is thought to be directly applied to the basilar membrane at its generation location on a cycle-by-cycle basis, consequently amplifying the sound-induced basilar membrane vibration and boosting hearing sensitivity (Dallos et al, 2008; de Boer, 1995b; Dong and Olson, 2013; Hudspeth, 2014; Liu and Neely, 2009; Reichenbach and Hudspeth, 2014). …”

Human cochlear hydrodynamics: A high-resolution μCT-based finite element study

“…Varin and Petrov (2008) and Reichenbach and Hudspeth (2014) provided the mathematical formalism to describe the surface wave that rise at the interface between BM soft tissue and endolymph. The perilymph is generally considered incompressible and the bone infinitely stiff.…”